Maths Made Easy Forums Standard Formulae & Equations Simultaneous Equations

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• #14095
Keymaster
Post count: 802

Solve simultaneously: 2x + y = 8, y = 4x – 10.

substitute y = 4x – 10 into second equation
2x + (4x – 10) = 8
6x – 10 = 8
6x = 18
x = 3

y = 4(3) – 10
y = 12 – 10
y = 2
∴ x = 3, y = 2

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Keymaster
Post count: 802

Solve: 3x – 5y = 28 and x + 4y = 15

multiply the second one by 3 to make the x’s the same

3x + 12y = 45  –
3x – 5y = 28

3x – 3x + 12y – -5y = 45 – 28

17y = 17

y = 1

x + 4(1) = 15

x + 4 = 15

x = 11

∴ x = 11, y = 1

Keymaster
Post count: 802

Solve simultaneously: 2x – 4y = 2, x = -2y + 9.

substitute the second equation into the ‘x’ of the first one

2(-2y + 9) -4y = 2
-4y + 18 – 4y = 2
-8y = -16
y = 2

x = -2(2) + 9
x = -4 + 9
x = 5

x = 1, y = 5

Keymaster
Post count: 802

Solve simultaneously: 7a + 3b = 4, 5a + 2b = 3.

7a + 3b = 4    ×2
5a + 2b = 3    ×3

14a + 6b = 8    –
15a + 6b = 9
-a = -1
a = 1

7(1) + 3b = 4
7 + 3b = 4
3b = -3
b = -1
∴ a = 1, b = -1